 02513 M. Cassandro, P.A. Ferrari, I. Merola, E. Presutti
 Geometry of contours and Peierls estimates in d=1 Ising models
with long range interactions
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Dec 11, 02

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Abstract. Following Fr\"ohlich and Spencer, \cite{FS}, we study one
dimensional Ising spin systems with ferromagnetic, long range
interactions which decay as $xy^{2+\alpha}$, $0\leq
\alpha\leq 1/2$. We introduce a geometric description of the spin
configurations in terms of triangles which play the role of
contours and for which we establish Peierls bounds. This in
particular yields a direct proof of the well known result by Dyson
about phase transitions at low temperatures.
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